Form factors are matrix elements of local operators between multi-particle states in quantum field theory. They can be used to compute correlation functions and other important quantities using spectral representation. Recently a breakthrough was achieved in the construction of form factors of the E7 model [1], which describes the scaling region of the tricritical Ising model in one spatial dimension. The aim of project is to build upon this foundation to provide a systematic construction of many-particle form factors as completely as possible. This is possible using the form factor bootstrap, which exploits the integrability of the model and requires the solution of complex analytic function equations (a particular sort of Riemann-Hilbert problem). The explicit solution can be checked against the partial results obtained in [1]  and also verified using the truncated conformal space approach [2]. The problem requires background in quantum field theory and complex analysis, and uses a heavy dose of symbolic computations as well as some numerical linear algebra.

[1]  A.C. Cubero, R.M. Konik, M. Lencsés, G. Mussardo, and G. Takács: Duality and form factors in the thermally deformed two-dimensional tricritical Ising model. SciPost Physics 12, 162 (2022)
[2]  D.X. Horváth, K. Hódsági, and G. Takács: Chirally factorised truncated conformal space approach. Computer Physics Communications 277, 108376 (2022)